The present disclosure relates to circuit modeling, and more specifically, to circuit modeling to determine the number of simulations required for characterizing intra-circuit variations.
Conventional technologies provide analysis techniques to characterize the effect of variations in transistor circuits. One method to characterize the effects of variation in a circuit uses a Monte-Carlo method of generating samples from the distribution of values of selected device parameters, applying those sample values in a plurality of circuit simulations, making circuit measurements during simulation and using a sensitivity analysis to compute the measurement variation of the circuit. The entire process requires N simulations, where N is the number of Monte Carlo sample cases required to meet a specified accuracy. Typically, N is on the order of 1,000 to 100,000 simulations.
Another method to characterize the effect of variations in a circuit is to simulate the circuit at nominal condition and make measurements. Then, for each device in the circuit and for each device parameter of a device, independently vary a selected device parameter away from nominal and simulate the circuit, making measurements to obtain measurement sensitivity, si to the variation of the selected device parameter. Commonly used methods to calculate sensitivity si include:si=(ppso,i−pneg,i)/2/pnom, orsi=(ppos,i−pnom)/pnom 
where pnom, ppos,i and pneg,i are measurements of p at nominal condition, setting selected device parameter i to positive sigma and negative sigma respectively. The overall sensitivity is then calculated by:
      s    total    =                    ∑                  i          =          1                N            ⁢              s        i        2            
where N is the number of devices.
The entire process requires c·N+1 simulations, where c is the number of selected device parameters to vary for a single device.
An alternative method to reduce the number of simulations is presented herein.